complementary adj.

late 14c., "means of completing; that which completes; what is needed to complete or fill up," from Old French compliement "accomplishment, fulfillment" (14c., Modern French complément), from Latin complementum "that which fills up or completes," from complere "fill up," from com-, here probably as an intensive prefix (see com-), + plere "to fill" (from PIE root *pele- (1) "to fill").

From c. 1600 as "full quality or number, full amount;" musical sense of "simple interval that completes an octave from another simple interval" is from 1873. In 16c. also having senses which were taken up c. 1650-1725 by compliment.

adjective and noun word-forming element, in most cases from Latin -arius, -aria, -arium "connected with, pertaining to; the man engaged in," from PIE relational adjective suffix *-yo- "of or belonging to." The neuter of the adjectives in Latin also were often used as nouns (solarium "sundial," vivarium, honorarium, etc.). It appears in words borrowed from Latin in Middle English. In later borrowings from Latin to French, it became -aire and passed into Middle English as -arie, subsequently -ary.

"a complementary relation or situation," 1908, a term in physics, from complementary + -ity.